论文标题
零gromov学位 - 平滑曲线的不变性
Degree zero Gromov--Witten invariants for smooth curves
论文作者
论文摘要
对于平滑的投影曲线，我们为其Gromov生成系列的封闭公式 - 属于$ g $和零度的不变性。众所周知，这些不变性的计算可以简化为$λ_g$和$λ_{g-1} $积分的$λ_g$和$λ_{g-1} $的计算。 $λ_g$积分的封闭公式由Faber和Pandharipande证明的$λ_G$猜想给出。我们在本文中计算$λ_{g-1} $积分，通过求解与复杂投影线相关的环路方程的零限制。
For a smooth projective curve, we derive a closed formula for the generating series of its Gromov--Witten invariants in genus $g$ and degree zero. It is known that the calculation of these invariants can be reduced to that of the $λ_g$ and $λ_{g-1}$ integrals on the moduli space of stable algebraic curves. The closed formula for the $λ_g$ integrals is given by the $λ_g$ conjecture, proved by Faber and Pandharipande. We compute in this paper the $λ_{g-1}$ integrals via solving the degree zero limit of the loop equation associated to the complex projective line.
